Identi fi cation of reservoir fractures on FMI image logs using Canny and Sobel edge detection algorithms
Mina Shafiabadi, Abolghasem Kamkar-Rouhani*, Seyed Reza Ghavami Riabi, Amin Roshandel Kahoo, and Behzad Tokhmechi
School of Mining, Petroleum and Geophysics, Shahrood University of Technology, Shahrood, Iran Received: 30 December 2019 / Accepted: 30 October 2020
Abstract.Because of the significant impact of fractures on production in hydrocarbon reservoirs, identification of these phenomena is a very important issue. Image logs are one of the best tools for revealing and studying fractures in reservoir and researcher can get lots of information about geological features in wells, by studying and analyzing these logs. In this research, two approaches have been used to determine the fractures in two wells A and B located in one of the oilfields in southwest of Iran. In thefirst approach, using Geolog software (version-7), after processing and correction of raw image log data, the number, position, dip, extension, layering, density and expansion of fractures have been identified. In the second approach, considering that the fractures in FMI images have edges, the Canny and Sobel filters as edge detection operators in image processing have been used to detect fractures in these images.
1 Introduction
Fractures are one of the important complications in reser- voir heterogeneity related tofluidflow and are more charac- teristic of large carbonate oilfields (Rezaie, 2008). The term fracture refers to any physical breakdown or discontinuity in the rock that is above the threshold of rock resistance.
Fractures include joints and faults (Zahrabzadeh, 2009).
Natural fractures control the behavior of the reservoir.
When the fractures are open, they create pathways for the movement of hydrocarbons to the well, and may even convert low permeability tanks into high-yielding samples.
Conversely, when the fractures are closed or cemented, they act as a barrier against the movement of hydrocarbons towards the well. This dual behavior of fractures makes it necessary to identify them (Javidet al., 2012). Direct and indirect methods for identifying fractures include the use of seismic sections, petrophysical logs, well testing, flower blasting, and descriptions of cores and image logs (Tingay et al., 2008). Seismic sections have low resolution for detec- tion of fractures but normally identify large-scale faults (Tokhmechi, 2009). Cores are the main source of informa- tion for small scale fractures. In addition, the cores for study of the fractures have three major limitations: high cost, low recycle at broken intervals and core shift during core sampling, while such limitations do not exist in image logs.
The image logs present high-resolution virtual images of
well walls that are capable of displaying delicate wall phenomena (Kulander et al., 1987). Image analysis began with the start of its use in 1986. Since then, many studies have begun to identify fractures on these logs. Torres et al.(1990)proposed a method based on Hough transform to detect the amplitude and phase of the fracture sine curve and the gradient corresponding to the fractures. This method is not the perfect response for interpretation and analysis of the fractures (Torreset al.1990).Ye and Baviler (1998) proposed a method based on Fourier transform to separate the padding and heterogeneous plates of each other. However, this method works weak for all the carbon- ate reservoirs (Ye and Baviler, 1998).Wang (2005)used the Valley-edge algorithm tofind fractures in the rocks without using threshold values. By this way, he detected the edges of the Charge Coupled Device (CCD) images taken from rocks. A multi-scale technique was used in the Wang’s algorithm for detecting the edges (Wang, 2005). Wang et al. (2007) provided a method based on edge detection and backup machines (Wang et al., 2007). Assous et al.
(2014) represented a new algorithm for detection of plane features on micro-resistance images of a well in a report titled“Automatic detection of plane features in image logs”. To separate the sinusoidal plane features, they also relied on information of the edges in the main part of their work (Assous et al., 2014). Considering the importance of frac- tures and problems in image interpretation, the purpose of this study is to introduce and apply image process- ing techniques and edge detection algorithms in image
* Corresponding author:kamkar@shahroodut.ac.ir
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
https://doi.org/10.2516/ogst/2020086
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processing called Canny and Sobel algorithms to identify fractures in image logs. The purpose of this study is to use the Canny and Sobel algorithms to find the edges of the fracture and finally compare the two methods tofind the best algorithm to do this.
1.1 Imaging logs
In 1985, Schlumberger introduced the Formation Micro Scanner (FMS) service. The FMS sonde consists of four orthogonal imaging pads each containing 16 microelec- trodes that are in direct contact with the borehole wall during the recording. The tool works by emitting a focused current from the four pads into the formation. Electrical imaging device FMI (Formation Micro Imager) is the second generation of electrical imaging devices that was produced in 1991 by Schlumberger Petroleum Company.
This device was designed to increase the wall cover of the well and to obtain a more coherent image than the FMS (Javidet al., 2012). The structure of the microprocessor is such that the pads andflaps are each mounted on 24 copper electrodes in two rows. The device consists of 192 electrodes with an effective diameter of 2 inches (Fig. 1). This machine, with 80% borehole coverage, produces high quality images. It is capable of analyzing very thin layers and detecting the type offine structures such as cross-layers and stylolites, veryfine fractures and distribution analysis of complex reservoirs (Schlumberger, 2004).
In general, an image log is taken cylindrically from the wellbore; for interpretation and observation, the image is opened and flattened and its geographic directions are determined (Fig. 2). Then, the plate structures that cut the wall of the well horizontally, in the form of sine curves with the following general equation (Rider, 1996):
y¼AsinðXþBÞ þC; ð1Þ whereA=RtanuandB ¼p2b.
In equation(1),Ris the well radius,uis the dip angle, b is the azimuth and C is the sinusoidal position in the image.
The processes performed on the images are divided into two categories:
A: The fundamental corrections necessary for electrical image logs include depth correction, speed correction, correction of broken and disabled pads, and so on.
B: Improving image quality processing, which can be equalization and image normalization.
By interpreting and processing these images, parameters such as layering, fracture, stylolite, and fault can be detected (Serra, 1984,1989).
2 Geological setting
The study area is one of the oilfields in southwest of Iran.
It is situated in Zagros belt, which extends in northwest- southeast direction. This fold-thrust belt extends about 2000 km from southeastern Turkey through northern
Syria and Iraq to western and southern Iran. The study field is located in Dezful embayment of Zagros basin in southwest of Iran (Alavi, 2004). Geological history of this basin includes long time subsidence and deposition, which has interrupted by short time uplift. Folding process of this basin occurred in Miocene and Pliocene and continued until now that led to forming long anticlines (Mottie, 1995).
In this research, image logs or data as well as other relevant data and information from two wells within Gachsaran oil field, located in southwest of Iran, have been selected (Fig. 3). Processing and interpretation of these data have been carried out in Geolog software. The Gachsaran oilfield is an elongated doublyplunging anticlinal structure with dimension of 70 km length and 6–15 km width, and it is considered as one of the most important productive oil fields in the Oligocene–Lower Miocene carbonate horizons and the Middle Cretaceous carbonate horizons (Fig. 4) (Mottie, 1995).
3 Methodology
As a result of the processing the FMI images from wells A and B, the sinusoidal curves of the closed fractures are displayed as clear lines and open fractures as dark lines and induced fractures due to drilling operations as Fig. 1. View of the FMI imaging device (Schlumberger, 2005).
Fig. 2. The collision plates with well walls (fractures or layers) are represented in the image logs as sinusoidal curves (Serra, 1989).
perpendicular to the layering (Fig. 5). In the image logs, faults are complications such as fractures, with the difference that the displacement of the plates in the faults is more. Although fault detection is very important in image logs, but due to the low diameter of the well, this phenomenon is rarely identifiable (Rider, 1996). As shown inFigure 6, the fracture planes are seen in the image (sine lines dark and light); They are selected by the arrows in the image as an open fracture (dark lines) or a closed fracture (the light lines) and the observed fault which are identified as blue, red, and pink sinuous curves with their dip and azimuth, respectively. Due to the dissolution of the well wall caused by the drilling fluid, the wall of the well may breakout. Therefore, the loosening of the well wall prevents full attachment of the pad to the wall, and at all these inter- vals, there is a black image. An example of a wellbore break- out is seen in well B at a depth of 2365–2368 m in the followingfigure that is confirmed by the caliper logs referred to by arrows (Fig. 7). After studying these two wells, a total Fig. 3. Location map of the studied oilfield in the Dezful Embayment of southwest Iran. The main geological and structural subdivisions of SW part of Iran are also shown and the location of the Dezful Embayment in this framework is marked (Mehrabiet al., 2013).
Fig. 4. Stratigraphic column of the southwestern Iran (Mottie, 1995).
of 262 fractures in well A and 60 fractures in well B were observed as a result of manual interpretation. Moreover, the open fractures were distinguished from the closed frac- tures in this study so that 47 open fractures and 214 closed fractures were identified in well A and 13 open fractures and 46 closed fractures were recognized in well B as a result of manual interpretation. InTable 1, the results obtained from the main interpretation of the wells made with the help of Geolog software are shown for comparison. As can be seen
from these two interpretation results shown inTable 2, no difference is seen between the open fractures in well B and the closed fractures in well A. However, the number of open fractures in well A identified by these two interpretation results vary by“1” difference. Similarly, a difference of“2” exists between the number of the closed fractures in well B are seen between these two interpretation results. After identification of fractures and considering that the number of fractures in each region is high, we draw these fractures (a) (b) (c)
Fig. 5. Example of fractures in wellbore image logs: (a) Drilling Induced Fractures (DIF), (b) closed fractures, and (c) open fractures.
Fig. 6. Example of closed and open fractures and faults in the FMI image of well B.
in the stereo diagram to obtain their statistical maxima. In this study, the total trend of fractures was investigated by plotting the rose diagram. With regard to the general trend of fractures, it can be concluded that the dominant frac- tures (open and closed) in well A have northeast-southwest trends, and a general east-west trend can be seen in well B (Fig. 8). Figure 9 demonstrates the general trend of the faults from the FMI images taken from wells A and B.
The pink sinusoidal curves in this figure displayed by the arrow indicate the plane of fault detected at wells A and B. The fault dip in well A is 19° with azimuth 16° from north to east. However, in well B, the fault dip is 69°with azimuth 357°from east to west. According toFigure 9, the general trend of the fault in well A is approximately north- west-southeast and the trend of the fault in well B is approximately northeast-southwest.
4 Edge detection techniques
Edge detection means the process of detecting and locating sharp brightness discontinuities in an image. Discontinuities are sudden changes in the brightness of pixels that deter- mine the boundary of the objects in the image (Clerk Maxwell, 1868; Gonzalez and Woods, 2002). Revealing the edges in images with noise is a difficult task because both the noise and the edges contain high frequencies.
Trying to reduce the noise of the images by melting the image will cause the edges to fail. Edge detector operators that reduce noise also reduce the accuracy of the edges that are visible due to changes in the image (Maini and Aggarwal, 2011). Generally, different edge detection methods are classified into two categories: gradient-based methods and Laplacian-based methods.
4.1 Gradient-based techniques
Edge detection methods can be classified into directional and non-directional or gradient-based operators. Direc- tional operators use two masks and two convolutions.
While non-directional use single mask and convolution but they are sensitive to noise due to gradient nature of the operators. Gradient-based detection methods reveal edges by searching for the maximum or minimum of the first derivative in the image (Gonzalez and Woods, 1992).
4.2 Laplacian-based techniques
In the Laplacian-based detection method, the location of the zero crossing of the second derivative of the image is searched for and defined as follows:
r2f xð yÞ ¼@2fðxyÞ
@x2 þ@2fðxyÞ
@y2 : ð2Þ
Among the most important edge detectionfilters that are the basis of theirfirst derivative work, we can refer to the Roberts, Prewitt, Canny and Sobelfilters, and the second derivative filters can also be used to describe the Marr- Hildreth and LOGfilter (Gonzalez and Woods, 2002).
4.2.1 Sobel edge detection operator
The Sobel edge detection method is introduced by Sobel (1970). The Sobel operator also uses thefirst derivative to find the edges of the image. This edge is one of the weakest edges, and can only detect edges with high light intensity variations. The Sobel technique performs a 2-D spatial gradient quantity on an image, and thus, highlights regions of high spatial frequency that correspond to edges (Sobel, 1970). In general, it is used tofind the estimated absolute gradient magnitude at each point in n input gray-scale image. In conjecture, at least the operator consists of a pair of 33 complication kernels as given in the tables shown in Figure 10. The gradient magnitude is given by Gonzalez and Woods (1992):
j j ¼G ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G2xþG2y
q ; ð3Þ
and typically, an approximate magnitude is computed using:
jGj ¼ jGxj þ jGyj: ð4Þ The angle of orientation of the edge (relative to the pixel grid) giving rise to the spatial gradient is given by:
uðx:yÞ ¼arctanðGx=GyÞ: ð5Þ
4.2.2 Canny edge detection operator
In industry, the Canny edge detection technique is one of the standard edge detection techniques. It wasfirst created by John Canny in his Master’s thesis at MIT in 1983, and still outperforms many of the newer algorithms that have been developed (Owens, 1997). Canny algorithm is very sophisticated and, of course, with high precision results that Fig. 7. An example of displaying the breakout of the well in the
FMI image of well B and the changes made in the caliper logs.
Well A Well B
Fig. 8. Display of the general trends of fractures in two wells A and B.
Table 1.A comparison of the number of fractures obtained from manual interpretation with main interpretation.
Type of fractures Manual interpretation
results
Main interpretation results
A B A B
Open fractures 47 13 48 13
Closed fractures 214 46 214 48
Faults 1 1 1 1
Total 262 60 263 62
Table 2.Comparison between Sobel and Canny edge detection techniques.
Method Sensitivity Operation Advantage Disadvantage
Sobel operator Medium Maximum of edges are identified with respect to perpendicular angle
Finding of smooth edges, used for image segmentation, simplicity
Computation time is high compare to Robert operator, less sensitive to noise high compare to Robert operator Canny Operator High Used to eliminate the
noise and tofind the effective edges
Finding the error rate is high, performance is good, used for image enhancement, smooth noise, good
localization
High computation time, complex process, false zero crossing.
will take a long time to implement. The algorithmic steps are as follows (Gonzalez and Woods, 1992;Muthukrishnan and Radha, 2011):
1. Removal of noise, unwanted textural artefacts and unwanted edges, through Gaussian smoothening of the image data.
2. Finding Gradients; after smoothing the image next step is to find the strength of edge by taking the gradient of the image. Sobel operator is used to perform 2-D spatial gradient measure on an image.
The edges should be marked where the gradients of the image have large magnitudes,finding the gradient of the image by feeding the smoothed image through a convolution operation with the derivative of the Gaussian in both the vertical and horizontal direction.
3. Non-maximum suppression; only local maxima should be marked as edges. Finds the local maxima in the direction of the gradient, and suppresses all others, minimizing false edges.
4. Double threshold; potential edges are determined by thresholding, instead of using a single static threshold value for the entire image, the Canny algorithm intro- duced hysteresis thresholding, which has some adaptively to the local content of the image. There are two threshold levels, th, high and tl, low where th > tl. Pixel values above the th value are immedi- ately classified as edges.
5. Edge Tracking by Hysteresis. Final edges are deter- mined by suppressing all edges that are not connected to a very strong edge.
5 Results and discussion
In this section, the Canny and Sobel edge-detection algo- rithms are implemented in MATLAB environment tofind the edges of fractures, and therefore, to identify the frac- tures on the FMI image logs. Thefirst step in this research
is to introduce and define the input image in the MATLAB software. The input image is a dynamic and normalized image originally generated from the FMI raw material data.
The existence of vertical white lines on the image that has been made after correction in the Geolog software, causes the discontinuities of the images to appear, and poses a unified fragmentation pixel accumulation. Therefore, using the Geolog software, these lines are removed from the image and the image is continuously added. Since the color images are composed of three Red, Green and Blue (RGB) color matrices, these color images are converted to a gray-scale images to reduce the volume of operations, so that we can display the image with only one matrix. On the FMI imaging screens, this filter is applied throughout the two wells A and B (Fig. 11).
5.1 Removal of noise from images
Noise contained in image is smoothed by convolving the input imageI(i,j) with Gaussian FilterG. Mathematically, the smooth resultant image is given by
F ið Þ ¼;j GI ið Þ:;j ð6Þ An approach to noise reduction in the image logs is to use the Non-Local Minimum (NLM) filter. The NLM filter is a commonfilter for processing medical images. The window size of this filter varies depending on the brightness of the
Well A Well B
Fig. 9. The general trends of faults detected on the FMI logs obtained from wells A and B.
G
xG
yFig. 10. Masks used by Sobel operator (Gonzalez and Woods, 1992).
image. The NLM filter is implemented by applying equations(7)–(10)(Ergin and Kilinc, 2014):
NLMðI qð ÞÞ ¼X
8qg
w pð qÞIðqÞ; ð7Þ
0w pð qÞ 1 X
8qg
pq
ð Þ ¼1; ð8Þ
where,I(q) represents a 2D image,pis the desired pixel in the image to perform thefiltering operation,qis the pixel in the neighboringg of the research window, andw(p,q) is also called the weight function, which in the relation, the production of its components is shown:
w pð qÞ ¼ 1
zðpÞe d pqð Þh2
; ð9Þ
where d is the Euclidean distance between the p and qpixels;his called the continuous kernel, which controls the reduction of the exponential function; and z(p) is the normalization constant calculated by the following equation.
z pð Þ ¼X
8q
e d pqð Þh2
: ð10Þ
5.2 Finding gradients
In this step we detect the edges where the change in grays- cale intensity is maximum. Required areas are determined with the help of gradient of images. Sobel operator is used to determine the gradient at each pixel of smoothened image (Gonzalez and Woods, 2002):
Di ¼
1 0 þ1 2 0 þ2 1 0 þ1
and Dj¼
þ1 þ2 þ1 2 0 þ2 1 2 1 : These Sobel masks are convolved with smoothed image and giving gradients iniandjdirections:
Gi ¼DiF ið;jÞ and Gj ¼DjF ið Þ:;j ð11Þ Therefore, edge strength or magnitude of gradient of a pixel is given by
G¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G2i þG2j
q : ð12Þ
The direction of gradient is given by u¼arctan Gj
Gi : ð13Þ
5.3 Non-maximum suppression
Non maximum suppression is carried out to preserve all local maxima in the gradient image, and deleting every- thing else this results in thin edges. For a pixelM(i,j):
Firstly round the gradient direction u nearest 45°, then compare the gradient magnitude of the pixels in positive and negative gradient directionsi.e.If gra- dient direction is east then compare with gradient of the pixels in east and west directions sayE(i,j) and W(i,j) respectively.
If the edge strength of pixel M (i, j) is largest than that ofE (i, j) and W(i, j), then preserve the value of gradient and markM(i,j) as edge pixel, if not then suppress or remove.
5.4 Hysteresis thresholding
Thresholding is the first step in most image processing systems and the simplest method of image segmentation.
At this point, the imagefield is separated from the objects by finding a threshold (Huang and Wang, 2008).r is the standard deviation parameter of the gaussianfilter and its value isfixed as per the degree of noise present in the input image (Bland and Altman, 1996; Gonzalez and Woods, 1992) are used. For a pixel M(i,j) having gradient magni- tudeGfollowing conditions exists to detect pixel as edge:
IfG<tlowthan discard the edge.
IfG>thighkeep the edge.
Iftlow<G < andthigh and any of its neighbors in a 3 3 region around it have gradient magnitudes greater thanthigh, keep the edge.
If none of pixel (x, y)’s neighbors have high gradient magnitudes but at least one falls between tlow and, thighsearch the 55 region to see if any of these pixels have a magnitude greater than thigh. If so, keep the edge.
Else, discard the edge.
In this research, we use two thresholds (high and low thresholds) as follows:
(a) (b) (c)
Fig. 11. Conversion of (a) the FMI log to (b) the gray-scale image, and (c) the black and white (binary) image.
Thresholds ¼ ½0:3;0:4; r ¼ ffiffiffiffiffi p12
:
The reason for using this Terscheld range in this study was that the lower the thresholds such as Th = [0.1, 0.2] applied to the image, the more edges would appear other than the fractures. The higher the thresholds such as Th = [0.7, 0.9]
are applied to the image, the edge of the sinusoidal curve of the fractures is removed. As a result, the most moderate Terscheld in this study (Th = [0.3, 0.4]) was selected so that neither the many edges of the fractures were removed nor the many edges other than the fractures appeared.
5.5 The edge detection result and analysis
Since color plays an important role in the analysis of images and color images are more informative than the gray ones, thus, in this study, the Canny edge algorithm operations
are applied to the color images to achieve a more favorable result.Figure 12shows the results of the closed fracture of FMI images in wells A and B at along with the changes made the Canny algorithm operation and its edges.
Figure 13shows the results of the Canny algorithm opera- tion, along with its changes on the borehole breakout observed at a depth of 2432–2434 m in well B. Figure 14 shows the results of the closed fracture of FMI images in wells A and B at along with the changes made the Sobel algorithm operation and its edges. Figure 15 shows the results of the Sobel algorithm operation, along with its changes on the borehole breakout observed at a depth of 2432–2434 m in well B.Figure 16shows the results of the comparison of applying the Canny algorithm with the Sobel algorithm on the fault in the FMI images obtained from well B. Every edge detection method has its own constraints and merits, and to find an appropriate edge
(a) (b) (c)
Fig. 12. Edge detection results using the Canny algorithm on closed fractures in wells A and B: (a) original image, (b) apply the Canny edge algorithm, (c) display the edges.
(a) (b) (c)
Fig. 13. Edge detection results using the Canny algorithm on breakout in well B: (a) original image, (b) apply the Canny edge algorithm, (c) breakout display with edge results.
(a) (b) (c)
Fig. 14. Edge detection results using the Sobel algorithm on closed fractures of FMI images in wells A and B: (a) original image, (b) apply the Sobel edge algorithm, (c) display the edges.
(a) (b) (c)
Fig. 15. Edge detection results using the Sobel algorithm on breakout in well B: (a) original image, (b) apply the Sobel edge algorithm, (c) breakout display with edge results.
(c) (b)
(a)
Fig. 16. (a) Fault on the FMI log from well B, (b) the result of applying the Sobel operator, and (c) the result of applying the Canny operator on the FMI image.
detection algorithm for a particular case, we must imple- ment these edge detection algorithms to get the desired results and to find the appropriate one. The Canny algorithm, due to the more detailed presentation of frac- tures, in comparison with the Sobel algorithm, has a better performance on the FMI images, and has been capable of revealing the sinusoidal curves of the fault and open and closed fractures to a large extent. The comparison results of Canny and Sobel edge detection algorithms are shown inTable 2.
6 Conclusion
Image logs are among the powerful tools that are used in the study of hydrocarbon reservoirs to identify fractured zones in the walls of wells. Two approaches were taken to identify fractures on FMI logs. In thefirst approach, after loading the FMI data from two wells, situated in an oilfield in southwest of Iran, in the Geolog software, various correc- tions and processing steps were made to the images. As a result, two static and dynamic images were obtained that indicate the types of fractures and breakouts in the two wells. In the second approach taken in this study, we used the Canny and Sobel edge detection algorithms so that we could show the performance of these edge detectors on the FMI log to identify fractures. The Sobel algorithm indicates very weak margins and discontinuities. It also contains false margins, however, the Canny algorithm shows clean, almost continuous, and real edges strongly.
The result shows Canny operator is optimum even for noisy images. This operatorfills the gap between strong and weak edges of the image. Compared to other edge detection techniques, this operator is less fooled by specious noise.
In Sobel edge detection method, it looks for both horizontal and vertical edges independently then represents them together. As a result, the proposed method can be a suitable solution for identifying fractures in electrical image logs.
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